What is the factors for #x^3 + 3x^2 - x - 3#?

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Answer 1 · 2015-05-02T12:26:58

#x^3 + 3x^2 - x - 3#

We can make groups of 2 terms like this:

#(x^3 + 3x^2) - (x + 3)#

# = x^2(x + 3) -1(x+3)#

#=(x+3)# is common to both the terms

#=(x+3)(x^2 - 1)#

#=(x+3)(x^2 - 1^2)#

We know that #color(blue)(a^2 - b^2 = (a+b)(a-b)#

# = color(green)((x + 3)(x+1)(x - 1)#

#x+3 ; x+1; x-1# are the factors of #x^3 + 3x^2 - x - 3#